A beam is supported at its ends by supports w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the vertex of the parabola be at the lowest point $O(0,0)$ and the axis be vertical along the $Y$-axis. The equation of the parabola is $x^2 =

Vedclass · Accepted Answer

$2 \sqrt{6} \, m$

Vedclass · Answer

(A) Let the vertex of the parabola be at the lowest point $O(0,0)$ and the axis be vertical along the $Y$-axis. The equation of the parabola is $x^2 = 4ay$.The total span is $12 \, m$,so the ends are at $x = 6 \, m$ and $x = -6 \, m$. The maximum deflection at the centre is $3 \, cm = 0.03 \, m$. Thus,the parabola passes through $(6, 0.03)$.Substituting these coordinates into the equation: $(6)^2 = 4a(0.03) \implies 36 = 0.12a \implies a = \frac{36}{0.12} = 300$.The equation is $x^2 = 4(300)y = 1200y$.We want to find $x$ when the deflection from the top is $1 \, cm$. Since the total deflection is $3 \, cm$,the height from the vertex $O$ is $y = 3 \, cm - 1 \, cm = 2 \, cm = 0.02 \, m$.Substituting $y = 0.02$ into the equation: $x^2 = 1200(0.02) = 24$.Therefore,$x = \sqrt{24} = 2\sqrt{6} \, m$.

$A$ beam is supported at its ends by supports which are $12 \, m$ apart. Since the load is concentrated at its centre,there is a deflection of $3 \, cm$ at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection $1 \, cm$?

Similar Questions

Find the length of the latus rectum of the parabola $y = x \tan \alpha - \frac{g x^2}{2 u^2 \cos^2 \alpha}$.

If $\theta$ is the acute angle between the tangents drawn from the point $(1,5)$ to the parabola $y^2=9x$,then:

What is the equation of the tangent to the curve $x^2 = -4y$ at the point $(-4, -4)$?

If a normal chord at a point $t (\neq 0)$ on the parabola $y^2 = 9x$ subtends a right angle at its vertex,then $t =$

Find the minimum distance from the point $(0, c)$ to the parabola $y = x^2$,where $0 \leq c \leq 5$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module